Diffusion Posterior Sampling with Uncertain Forward Models

Diffusion posterior samplers reconstruct signals by combining a pretrained diffusion prior with a measurement likelihood specified by a forward model and a noise model. Calibration and reference data can characterize uncertainty in the forward model's parameters, such as blur kernels or detector responses. Fixing these parameters at estimated values leaves their uncertainty out of the likelihood, and parameter errors are thus absorbed into the reconstruction. We introduce an uncertainty-aware likelihood (UAL), a Gaussian approximation to the marginal likelihood obtained by integrating over the uncertain parameters. For each candidate signal, UAL propagates parameter uncertainty into a structured measurement covariance, reducing the quadratic penalty along residual directions that parameter variation can explain. Existing samplers can use UAL in their data updates while retaining their pretrained diffusion priors and sampling schedules. Under a fixed Gaussian nuisance model, we bound likelihood error from linearization and the resulting average divergence between the exact marginal and UAL posteriors. We compare samplers with and without UAL across six inverse problems spanning Gaussian and motion deblurring, CT, MRI, ultrasound, and fluorescence microscopy, and find improvements in reconstruction and ensemble prediction. UAL reduces geometric mean MSE by 9% to 20% across samplers in the main Gaussian-deblurring setting and by 51% to 92% in motion deblurring when non-blind samplers use the population-mean kernel. In motion deblurring, DAPS and PnP-DM with UAL also give 6.2 to 6.4 dB higher ensemble-mean PSNR than published BlindDPS and Fast Diffusion EM. On the ablation set, UAL outperforms trace-matched isotropic inflation for PnP-DM in both deblurring tasks; in motion deblurring, it also exceeds the best-tested fixed scalar data weighting by 3.3 dB for PnP-DM and 4.2 dB for DAPS in average PSNR.